Heavy Top Research Articles

Electroweak effects in the [formula omitted] mixing

We compute analytically the complete electroweak two-loop corrections to the B 0− B 0 mixing. These corrections fix the normalization of the electroweak coupling employed in the extraction of | V td | and reduce the theoretical uncertainty due to higher order electroweak effects from several percent to a few parts in a thousand. If the LO result is expressed in terms of G μ or of the MS coupling ĝ(Mz), the two-loop corrections are O(1%), the exact value depending on the mass of the Higgs boson. We discuss in detail the renormalization procedure and the scheme and scale dependence, and provide practical formulas for the numerical implementation of our results. We also consider the heavy top mass expansion and show that in the case at hand it converges very slowly.

Elementary theoretical description of the heavy symmetric top

A simple theoretical description of a symmetric top with one stationary point and subject to the action of the gravitational force is presented without the use of Lagrangian mechanics. Also no use is made of the Euler angles. The fact that the vectors of the angular momentum l, the angular velocity ω, and the symmetry axis ẽ3 are coplanar every instant of time is used to derive a closed set of equations for ẽ3 and l. The frequencies of pure “slow” and “fast” precession are calculated without solving the differential equations and a simple interpretation of the latter is given. Using energy conservation, the well-known differential equation for the angle θ between the symmetry axis and the surface normal is derived. The combination of precession and nutation is discussed for small nutation amplitudes.

Two-loop heavy top corrections to the b → sγ decay

We compute the two-loop corrections to the coefficient of the b ← sγ magnetic penguin present in the limits of heavy top and/or heavy Higgs. These kinds of corrections affect in a significant way the observables measured at LEP. On the contrary we find that, due to a numerical accident, the correction to BR( B → X s γ) is negligible (below the 1% level for any possible value of the Higgs mass) when the leading order result is expressed in the usual way in terms of the semileptonic BR(B → X c eν) .

The Euler–Poincaré Equations and Semidirect Products with Applications to Continuum Theories

We study Euler–Poincaré systems (i.e., the Lagrangian analogue of Lie–Poisson Hamiltonian systems) defined on semidirect product Lie algebras. We first give a derivation of the Euler–Poincaré equations for a parameter dependent Lagrangian by using a variational principle of Lagrange d'Alembert type. Then we derive an abstract Kelvin–Noether theorem for these equations. We also explore their relation with the theory of Lie–Poisson Hamiltonian systems defined on the dual of a semidirect product Lie algebra. The Legendre transformation in such cases is often not invertible; thus, it does not produce a corresponding Euler–Poincaré system on that Lie algebra. We avoid this potential difficulty by developing the theory of Euler–Poincaré systems entirely within the Lagrangian framework. We apply the general theory to a number of known examples, including the heavy top, ideal compressible fluids and MHD. We also use this framework to derive higher dimensional Camassa–Holm equations, which have many potentially interesting analytical properties. These equations are Euler–Poincaré equations for geodesics on diffeomorphism groups (in the sense of the Arnold program) but where the metric isH1rather thanL2.

Baryonic systems with charm and bottom in the bound-state soliton model

The binding energies of baryonic systems with baryon numberB=2, 3, and 4 possessing heavy flavor, charm, bottom, or top, are estimated within the rigid oscillator version of the bound-state approach to chiral soliton models. Two tendencies are noted: the binding energy increases with increasing mass of the flavor and with increasingB. Therefore, the charmed or bottom baryonic systems have a better chance of being bound than do the strange baryonic systems discussed previously.

Stationary configurations of a vortex filament in background flows

We investigate the three-dimensional configurations of a thin vortex filament embedded in background flows of an inviscid incompressible fluid, based on the localized induction approximation. An analogy is found between stationary configurations of a vortex filament in a steady flow and trajectories of a charged particle in a steady magnetic field. An analogy with trajectories of a sound ray in a steady low-Mach number flow is drawn as well. These analogies allow us to use the Lagrangian and Hamiltonian formalism of classical mechanics for calculating fully nonlinear forms of a vortex filament. The equations for the filament curve are integrable when the background flow has two spatial symmetries. Only integrable cases are explored in some detail. To illustrate the advantages of use of the analogy, we re-examine the invariant shapes of a vortex filament moving through a still fluid obtained by Kida (1981). Analogies of the Kida class with the motions of a heavy symmetrical top and a charged spherical pendulum in the field of a magnetic monopole are discussed. As next examples, we consider a point source (sink) and a line source (sink) flows. A filament takes the form of a non-uniform helix wound around a cone. The last example is a circular jet of a parabolic velocity profile. We construct a closed filament with azimuthal waves, lying on a plane orthogonal to the flow direction. Among them, an elliptic vortex ring is found to be distinct from higher waves.

Euler-Poisson equations and existence of quasi-periodic motions of heavy tops

We study the existence of quasi-periodic motions of an asymmetric heavy top by using two different approaches: the standard Moser-Weinstein theorem and an extended Liapounov center theorem. We take advantage of the multiple reversibility of the Euler-Poisson equations and are able to show that the extended Liapounov center theorem yields more normal modes than does the Moser-Weinstein theorem.

Implications of heavy top

Lecture at 23 ITEP Winter School. Manifestations of heavy top at low energies (K- and B-mesons) and high energies (Z and W physics) are discussed

Stabilization of the Inverted Linearized Pendulum by High Frequency Vibrations

In this note we give a simple geometrical picture that explains why an inverted pendulum is stabilized by high frequency vibrations.

Weak chaos in the asymmetric heavy top

We consider the dynamics of the slightly asymmetric heavy top, a non-integrable system obtained from the Lagrange top by breaking the symmetry of its inertia tensor. It shows signs of weak chaos, which we study numerically. We argue that it is a good example for introducing students to non-integrability and chaos.

Equivariant constrained symplectic integration

We use recent results on symplectic integration of Hamiltonian systems with constraints to construct symplectic integrators on cotangent bundles of manifolds by embedding the manifold in a linear space. We also prove that these methods are equivariant under cotangent lifts of a symmetry group acting linearly on the ambient space and consequently preserve the corresponding momentum. These results provide an elementary construction of symplectic integrators for Lie-Poisson systems and other Hamiltonian systems with symmetry. The methods are illustrated on the free rigid body, the heavy top, and the double spherical pendulum.

The Rotational Spectrum of the Benzene‐Carbonyl Sulfide Complex. A Contribution to the Theory of Internal Rotation with Heavy Tops

AbstractThe rotational spectra of the four isotopomers normal, d1, d6, 18O of the benzene‐carbonyl sulfide complex, C6H6 ‐ OCS, have been analyzed. The interpretation of the rotational spectra as quasi symmetric top spectra has been deduced from the internal rotation theory. Most probably the carbonyl sulfide is perpendicular to the plane of benzene with sulphur towards benzene. The distance between the centers of mass of the partners is 4.42 Å.

Implications of a heavy top in supersymmetric theories

In the context of the radiative electroweak symmetry breaking scenario, we investigate the implications of a heavy top quark mass, close to its infrared fixed point, on the low energy parameters of the minimal supersymmetric standard model. We use analytic expressions to calculate the Higgs masses as well as the supersymmetric masses of the third generation. We further assume bottom-tau unification at the GUT scale and examine the constraints put by this condition on the parameter space (tan β, α 3), using the renormalization group procedure at the two-loop level. For supersymmetry breaking scale varying in the range (250–1000) GeV we find only a small fraction of the parameter space where the above conditions can be satisfied, namely 1 ≤ tan β ≤ 2, while 0.114 ≤ α 3( M Z ) ≤ 0.125. We further analyse in brief the case where all three Yukawa couplings reach the perturbative limit just after the unification scale. In this case, due to the large corrections on the bottom mass from sparticle loops, the top-mass and tan β predictions are significantly lower than those estimated when such corrections were ignored.

O( ααsln mt2) non-universal corrections to the decay rate [formula omitted

The partial decay rate Γ(Z → b b) is significantly influenced by the mass of the top quark due to electroweak radiative corrections. The leading ∼ m t 2 and the next-to-leading contribution ∼ ln m t 2 are known to be numerically of similar size. In this work we calculate the QCD corrections to the logarithmic correction using the heavy top mass expansion. The O( αα s ln m t 2) corrections are of the same order as the QCD corrections to the quadratic top mass term, but of different sign.

Prospects for Higgs detection at LEP 2

Before LHC will turn on, LEP 2 will continue the search for Higgs particles, beyond the limits established by LEP 1. The LEP 2 collider could explore the Higgs mass range between 60 GeV and above 100 GeV, thus being complementary of LHC in the search for the Higgs particle(s). It is very important to search for a relatively light Higgs because, as consequence of the heavy top ( m t ∼ 170 GeV), the detection of a light Higgs at LEP 2 could be a first signal that there is an extended Higgs sector and physics beyond the Standard Model. In this paper I describe the experimental strategy designed to search for Higgs particles produced either via the Bjorken process ( e + e − h Z) or in pair ( e + e − h A). I summarize then the results for the expected mass regions explorable at LEP 2, as function of the center of mass energy and the luminosity provided to the experiments.

Corrections of order [formula omitted] to the Higgs decay rate [formula omitted

QCD corrections to the electroweak one-loop result for the partial width Γ(H → b b) are studied. For the decay channel into bottom quarks the rate is affected by a virtual top quark through electroweak interactions. The calculation of QCD corrections to this quantity is performed for an intermediate range Higgs mass in the heavy top mass limit. The leading correction of order O(G Fα sm t 2 is estimated. Numerically the contribution is of the size as the electroweak correction.

Bardeen anomaly and Wess-Zumino term in the supersymmetric standard model

We construct the Bardeen anomaly and its related Wess-Zumino term in the supersymmetric standard model. In particular we show that it can be written in terms of a composite linear superfield related to supersummetrized Chern-Simons forms, in very much the same way as the Green-Schwarz term in four-dimensional string theory. Some physical applications, such as the contribution to the g−2 of gauginos when a heavy top is integrated out, are briefly discussed.

LEADING TOP MASS CORRECTIONS OF ORDER ${\mathcal O} (\alpha \alpha_s m_t^2 /M_W^2)$ TO THE PARTIAL DECAY RATE $\Gamma (Z\to b\bar b)$

The order [Formula: see text] corrections to the partial decay rate of [Formula: see text] are computed using the heavy top mass expansion. They are given by the absorptive part of the corresponding three-loop Z self-energy diagrams. Our method provides an independent way to calculate the QCD corrections to the electroweak one-loop result for [Formula: see text] and our result represents another confirmation of the one recently published by Fleischer et al.

Classical geometric forces of reaction: an exactly solvable model

We illustrate the effects of the classical ‘magnetic’ and ‘electric’ geometric forces that enter into the adiabatic description of the slow motion of a heavy system coupled to a light one, beyond the Born–Oppenheimer approximation of simple averaging. When the fast system is a spin S and the slow system is a massive particle whose spatial position R is coupled to S with energy (fast hamiltonian) S · R , the magnetic force is that of a monopole of strength I (= adiabatic invariant S · R / R ) centred at R = 0, and the electric force is inverse-cube repulsion with strength S 2 – I 2 . Confining the slow particle to the surface of a sphere eliminates the Born–Oppenheimer and electric forces, and generates motion with precession and nutation exactly equivalent to that of a heavy symmetrical top. In the adiabatic limit the nutation is small and the averaged precession is precisely reproduced by the magnetic force. Alternatively, choosing the exactly conserved total angular momentum to vanish eliminates the Born–Oppenheimer and magnetic forces, and generates as exact orbits a one-parameter family of curly ‘antelope horns’ coiling in from infinity, reversing hand, and receding to infinity. In the adiabatic limit the repulsion of the ‘guiding centre’ of these coils is exactly reproduced by the electric force. A by-product of the ‘antelope horn’ analysis is a determination of the shape of a curve with a given curvature k and torsion T in terms of the evolution of a quantum 2-spinor driven by a planar ‘magnetic field’ with components k and T .

Bifurcation of liquid drops

The reduced energy momentum method of Simo et al. (1991) may be used to locate bifurcations of steady motions of conservative systems from symmetric steady motions. A family of functionals parametrized by the isotropy algebra can be used to characterize a symmetric relative equilibrium. A variation of the Equivariant Branching Lemma is used to construct a scalar equilibrium equation on an appropriate submanifold of the configuration manifold. This equation can be solved for the free parameter associated to the isotropy subalgebra to obtain stability and bifurcation results. Applications to three mechanical systems are considered: the heavy Lagrange top, the Riemann ellipsoids, and planar incompressible free boundary flow. The bifurcation analyses of the heavy top and the Riemann ellipsoids recapture the classical results of Routh and Riemann. The analysis of swirling planar flows establishes the existence of nonrigid steady motions of asymmetric fluid regions bifurcating from a rigidly rotating fluid disc and improves an existing formal stability result for the rigidly rotating disc. A common feature of these three examples is the existence of a range of angular velocities for which the symmetric steady motions are both (formally) orbitally and linearly stable and yet bifurcations to asymmetric steady motions occur.